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Name: \( \qquad \) Agbay, Kris May Gr.\&Sec.: \( \qquad \) Score: \( \qquad \) Date: \( \qquad \) \( 2121 / 25 \) MASTERY TEST 4.1 I. IDENTIFICATION: Read each description carefully and write what/who is being asked. \( \qquad \) 1. He is considered as the father of Trigonometry. \( \qquad \) 2. Give the 2 Greek words where the word Trigonometry came from \( \qquad \) 3. \( \qquad \) 4. He wrote the Almagest. \( \qquad \) 5. He wrote the first textbook to bear the title Trigonometry. \( \qquad \) 6. He discovered sine and cosine. \( \qquad \) 7. He discovered tangent. \( \qquad \) 8. They applied the methods \( \qquad \) 9. of analysis to trigonometry \( \qquad \) 10.

Ask by Carrillo Logan. in the Philippines
Feb 21,2025

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Answer

Here are the answers to the identification questions: 1. **Father of Trigonometry:** Hipparchus 2. **Greek Words for Trigonometry:** "Trigonon" (triangle) and "metron" (measure) 3. **(Missing Description)** 4. **Wrote the Almagest:** Claudius Ptolemy 5. **First Trigonometry Textbook:** Bartholomaeus Pitiscus 6. **Discovered Sine and Cosine:** Aryabhata 7. **Discovered Tangent:** Nasir al-Din al-Tusi 8. **(Missing Description)** 9. **Applied Methods to Trigonometry:** (Missing Description) 10. **(Missing Description)** Please provide the missing descriptions for questions 3, 8, 9, and 10 for complete answers.

Solution

Here are the answers to the identification questions based on the descriptions provided: 1. **He is considered as the father of Trigonometry.** **Answer:** Hipparchus 2. **Give the 2 Greek words where the word Trigonometry came from.** **Answer:** "Trigonon" (triangle) and "metron" (measure) 3. **(This question is missing a description; please provide it for an answer.)** 4. **He wrote the Almagest.** **Answer:** Claudius Ptolemy 5. **He wrote the first textbook to bear the title Trigonometry.** **Answer:** Bartholomaeus Pitiscus 6. **He discovered sine and cosine.** **Answer:** Aryabhata 7. **He discovered tangent.** **Answer:** Nasir al-Din al-Tusi 8. **They applied the methods.** **Answer:** (This question is missing a description; please provide it for an answer.) 9. **of analysis to trigonometry.** **Answer:** (This question is missing a description; please provide it for an answer.) 10. **(This question is missing a description; please provide it for an answer.)** If you have additional descriptions for questions 3, 8, 9, and 10, please provide them for complete answers.

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Extra Insights

1. Hipparchus 2. "Trigonon" (triangle) and "metron" (measure) 3. 4. Claudius Ptolemy 5. Bartholomaeus Pitiscus 6. Aryabhata 7. Hugh Montgomery 8. Indian mathematicians 9. Persian and Arab scholars 10.

Related Questions

8. Simplify without using a calculator. (8.1) \( \frac{\sin \left(180^{\circ}-x\right) \cdot \tan \left(360^{\circ}-x\right)}{\cos \left(80^{\circ}-x\right)} \times \frac{\cos \left(-180^{\circ}-x\right)}{\cos \left(360^{\circ}+x\right) \sin \left(360^{\circ}-x\right)} \) \( 8.2 \frac{\cos 135^{\circ} \sin 160^{\circ}}{\sin 225^{\circ} \cos 70^{\circ}} \) (8.3) \( \frac{\sin (-\theta)+\cos 120^{\circ}+\tan \left(-180^{\circ}-\theta\right)}{\sin ^{2} 225^{\circ}-\tan (-\theta)-\cos \left(90^{\circ}+\theta\right)} \) B.4 \( 4^{x} \frac{\sin 247^{\circ} \cdot \tan 23^{\circ} \cdot \cos 113^{\circ}}{\sin \left(-157^{\circ}\right)} \) (8.5) \( \frac{3 \cos 150^{\circ} \cdot \sin 270^{\circ}}{\tan \left(-45^{\circ}\right) \cdot \cos 600^{\circ}} \) 8.6) \( \frac{\tan \left(180^{\circ}-x\right) \cdot \sin \left(90^{\circ}+x\right)}{\sin (-x)}-\sin y \cdot \cos \left(90^{\circ}-y\right) \) \( 8.7 \frac{\tan 30^{\circ} \cdot \sin 60^{\circ} \cdot \cos 25^{\circ}}{\cos 135^{\circ} \cdot \sin \left(-45^{\circ}\right) \cdot \sin 65^{\circ}} \) 6.8) \( \frac{\tan \left(180^{\circ}-x\right) \cdot \sin \left(90^{\circ}-x\right)}{\cos \left(90^{\circ}+x\right)}-\frac{\cos \left(180^{\circ}-x\right)}{\sin \left(90^{\circ}+x\right)} \) \( 8.9 \frac{\sin 189^{\circ}}{\tan 549^{\circ}}-\frac{\cos ^{2}\left(-9^{\circ}\right)}{\sin 99^{\circ}} \) Solving trigonometric equations (no calculators) (1.) If \( \sin \mathrm{A}=\frac{-3}{5} \) and \( 0^{\circ}<\mathrm{A}<270^{\circ} \) determine the value of: \( 1.1 \cos A \) \( 1.2 \tan A \). (2.) If \( -5 \tan \theta-3=0 \) and \( \sin \theta<0 \), determine: \( 2.1 \sin ^{2} \theta^{\circ} \) \( 2.25 \cos \theta \) \( 2.3 \quad 1-\cos ^{2} \theta \) 3. If \( 13 \cos \theta+12=0 \) and \( 180^{\circ}<\theta<360^{\circ} \), evaluate: \( 3.2 \tan \theta \) \( 3.1 \sin \theta \cos \theta \) \( 3.3 \sin ^{2} \theta+\cos ^{2} \theta \). (4.) If \( 3 \tan \theta-2=0 \) and \( \theta \in\left[90^{\circ} ; 360^{\circ}\right] \), determine, the value of \( \sqrt{13}(\sin \theta-\cos \theta \) (5.) If \( \cos 52^{\circ}=k \) as illustrated in the diagram, determine each of the following i
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